(3x+4)(5x)(6x+8)x=

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Solution for (3x+4)(5x)(6x+8)x= equation: 


Simplifying
(3x + 4)(5x)(6x + 8) * x = 0

Reorder the terms:
(4 + 3x)(5x)(6x + 8) * x = 0

Remove parenthesis around (5x)
(4 + 3x) * 5x(6x + 8) * x = 0

Reorder the terms:
(4 + 3x) * 5x(8 + 6x) * x = 0

Reorder the terms for easier multiplication:
5x * x(4 + 3x)(8 + 6x) = 0

Multiply x * x
5x2(4 + 3x)(8 + 6x) = 0

Multiply (4 + 3x) * (8 + 6x)
5x2(4(8 + 6x) + 3x * (8 + 6x)) = 0
5x2((8 * 4 + 6x * 4) + 3x * (8 + 6x)) = 0
5x2((32 + 24x) + 3x * (8 + 6x)) = 0
5x2(32 + 24x + (8 * 3x + 6x * 3x)) = 0
5x2(32 + 24x + (24x + 18x2)) = 0

Combine like terms: 24x + 24x = 48x
5x2(32 + 48x + 18x2) = 0
(32 * 5x2 + 48x * 5x2 + 18x2 * 5x2) = 0
(160x2 + 240x3 + 90x4) = 0

Solving
160x2 + 240x3 + 90x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10x2'.
10x2(16 + 24x + 9x2) = 0

Factor a trinomial.
10x2((4 + 3x)(4 + 3x)) = 0

Ignore the factor 10.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(4 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 3
Set the factor '(4 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333
Solution
x = {0, -1.333333333, -1.333333333}

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